An Obama administration debate about whether to engage Vladimir Putin or treat him like a pariah has tilted in the engagement camp’s favor—even as critics and some officials worry that it’s become too easy for the Russian president to get a stature-enhancing meeting with U.S. leaders.

When Secretary of State John Kerry heads to Moscow on Tuesday for a planned sit-down with Putin, it will be his second visit to see the Russian leader since May. It also follows three face-to-face encounters between Putin and President Barack Obama since late September. Some critics of engagement fear that Putin has, in effect, used his military intervention in Syria to win a seat at the diplomatic table, while others doubt that the increased dialogue is achieving anything.

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“The skeptics are still skeptical,” said Evelyn Farkas, who departed as the Pentagon’s top official for Russia and Ukraine this fall and pushed for a generally harder line on Moscow than the White House has adopted. “You don't have any results yet for the engagement people.”

For now, sources say, Obama and Kerry in particular believe the costs of interacting with Putin are relatively low and that discussion—whose tone a senior administration official described as “not warm but not hostile,” and “businesslike”—is more likely than a freeze-out to yield progress on disputes over a peace deal for Syria and Russian aggression in Ukraine.

“The president has always said that he will work with Putin, he will talk to Putin, when it’s our responsibility to solve something really important on global security,” says a senior administration official.

The frequent meetings with Putin now contrast with the months after Russia’s March 2014 annexation of Ukraine's Crimean Peninsula. During that period, Obama spoke several times by phone with Putin but spurned face-to-face meetings. Pro-isolation officials held that Putin should change his aggressive behavior before meeting Obama and hoped that shunning him would diminish the prideful Russian on the world stage.

More recently, a pro-engagement camp spearheaded by Kerry has argued that ignoring Putin won’t change his behavior—and that, like it or not, the U.S. has to coordinate with Russia on global security issues.

“There’s no doubt that the Russian military intervention in Syria has given them a seat at the table” in the emerging Syria peace process, said Andrew Weiss, a Russia specialist at the Carnegie Endowment for International Peace who served on Bill Clinton’s National Security Council staff. “We can't wish that away. Putin has created facts that the rest of the world now has to reckon with—including John Kerry.”

Kerry last saw Putin on a mid-May visit to the Black Sea resort town of Sochi, where he spent hours talking to Russian officials about a range of security issues. Pro-Russian media outlets depicted that trip as a softening of the Obama administration's stance toward Putin.

Weiss called this week's Moscow visit “classic John Kerry.” He said the diplomat is “throwing himself into Syria diplomacy with total force and vigor,” much as he did in pursuit of the Iran nuclear deal and the failed effort to win a Middle East peace settlement, though he warned that the U.S. might lack diplomatic leverage because of Obama’s cautious approach to military involvement in the Syrian conflict.

Speaking with reporters in Paris last week, Kerry insisted that Russia “is playing a constructive and important role” when it comes to reaching a political agreement that could end Syria’s civil war.

But U.S. officials remain frustrated that Putin, who supports the regime of Syrian President Bashar Assad, continues to focus most Russian airstrikes on rebel fighters in Syria who are unaffiliated with the Islamic State but who post a more direct military threat to the Assad regime.

And they note that Putin has yet to honor a peace agreement Russia struck with European powers in February to end the conflict in Ukraine, fueled by pro-Russian separatists whom Moscow has aided with equipment and manpower. December 31 is the deadline for the implementation of that agreement, known as the Minsk accords, but Russia is far from meeting its provisions, which include the withdrawal of all foreign forces from Ukraine and full restoration of Kiev's control over its eastern border.

Writing recently in The American Interest, David Kramer, a George W. Bush State Department official who handled Russian and European affairs, complained that “by chasing after Russia’s leaders yet again … Kerry reinforces the impression the Obama administration has created throughout its tenure that we need Russia more than Russia needs us.”

Obama officials insist that’s not the case, arguing that Putin has been cornered by sanctions imposed after his annexation of Crimea and meddling in eastern Ukraine, and his thus-far inconclusive Syria intervention.

In an email, Kramer also noted that Obama boasted in his January State of the Union address about isolating Putin over his aggression in Ukraine, but has since met with the Russian leader several times—while making time for only a quick “pull-aside” with Ukraine President Petro Poroshenko.

Obama can compartmentalize his approach to Putin, the senior official said, by dealing with him in areas of possible agreement while pressuring him on points of conflict. The official pointed to the recent cooperation between Obama and Putin on a September 2013 deal to remove chemical weapons from Syria and on the July nuclear deal with Iran, even as they locked horns on other topics.

Obama’s last two meetings with Putin have been far more casual than the formal bilateral meeting they held at the United Nations in late September. At the mid-November G-20 summit in Antalya, Turkey, the two leaders “ran into one another” around a group luncheon “and agreed to have a quick word,” according to the senior official. That led to a 35-minute chat around a small table in a luxury hotel lobby that included National Security Adviser Susan Rice and a Putin aide. Television footage showed Obama and Putin leaning in, their faces about two feet apart, with intent expressions.

Last week, Kerry suggested that his main focus in Moscow will be the Syrian conflict, specifically winning Russian support for a peace settlement among the regime and rebel groups that would usher Assad from power. Putin has yet to commit to a timeline for Assad’s exit, a core demand of many rebel factions and outside powers such as Saudi Arabia and Turkey.

Obama says only a political settlement that guarantees Assad’s exit can end Syria’s civil war and isolate the Islamic State, also known as ISIS or ISIL, which has drawn strength from the Syrian conflict. The U.S. is open to a transition period for implementing a peace deal and holding elections during which Assad would be allowed to stay in power, but it is not clear for how long Obama would tolerate Assad’s continued reign.

"It may be that Kerry wants to look Putin in the eye and say, 'No kidding: What’s the plan for moving Assad out? Are you going to give him a dacha or what?" Farkas said. (Many observers speculate that Putin might offer his ally Assad sanctuary in Russia should the Syrian step down.)

Kerry’s visit comes ahead of a Dec. 18 meeting the U.S. is trying to arrange in New York City for the parties involved in the Syria peace talks. Last week, an array of rebel groups meeting in Saudi Arabia selected a delegation for any potential talks with the Assad regime, something Kerry called “an important step forward.” But Russia’s foreign ministry responded skeptically, questioning whether the rebels who attended the Saudi conference were representative of the opposition and complaining that their ranks included “terrorists.” Assad likewise reiterated on Friday that he refuses to “negotiate with terrorists,” a word he uses to describe all rebel groups in his country.

The U.S. official underscored that Kerry will also address the subject of Ukraine, which Vice President Joe Biden visited last week. That is likely to be a testy subject. The European Union could vote to extend Ukraine-related sanctions on Russia as soon as this week, according to European diplomats.

Putin blames the Ukrainians for failing to honor their end of the agreement, In a recent interview with the Italian newspaper La Repubblica. Russian Foreign Minister Sergei Lavrov bitterly complained about continued U.S. pressure on the subject.

“As long as Obama's deputy Joe Biden goes around Europe recommending continued sanctions against us without taking into account how Kiev is behaving under Western pressure, we will not be able to reach any understanding,” Lavrov told the paper.

U.S. officials concede that Kiev hasn’t behaved perfectly. But they say it's Russia and its nostalgia for it's superpower status that has become the main obstacle to a lasting peace in a conflict that has now claimed more than 9,000 lives on Europe’s eastern edge.